ExtendedArithmetic.GenericPolynomial 2022.187.1018

There is a newer version of this package available.
See the version list below for details.
dotnet add package ExtendedArithmetic.GenericPolynomial --version 2022.187.1018
NuGet\Install-Package ExtendedArithmetic.GenericPolynomial -Version 2022.187.1018
This command is intended to be used within the Package Manager Console in Visual Studio, as it uses the NuGet module's version of Install-Package.
<PackageReference Include="ExtendedArithmetic.GenericPolynomial" Version="2022.187.1018" />
For projects that support PackageReference, copy this XML node into the project file to reference the package.
paket add ExtendedArithmetic.GenericPolynomial --version 2022.187.1018
#r "nuget: ExtendedArithmetic.GenericPolynomial, 2022.187.1018"
#r directive can be used in F# Interactive and Polyglot Notebooks. Copy this into the interactive tool or source code of the script to reference the package.
// Install ExtendedArithmetic.GenericPolynomial as a Cake Addin
#addin nuget:?package=ExtendedArithmetic.GenericPolynomial&version=2022.187.1018

// Install ExtendedArithmetic.GenericPolynomial as a Cake Tool
#tool nuget:?package=ExtendedArithmetic.GenericPolynomial&version=2022.187.1018


A univariate, sparse, generic polynomial arithmetic library. That is, a polynomial in only one indeterminate, X, that only tracks terms with non-zero coefficients. This generic implementation has been tested and supports performing arithmetic on numeric types such as BigInteger, Complex, Decimal, Double, BigComplex, BigDecimal, BigRational, Int32, Int64 and more.

All arithmetic is done symbolically. That means the result a arithmetic operation on two polynomials, returns another polynomial, not some integer that is the result of evaluating said polynomials.

BigInteger Polynomial

  • Supports symbolic univariate polynomial arithmetic including:
    • Addition
    • Subtraction
    • Multiplication
    • Division
    • Modulus
    • Exponentiation
    • GCD of polynomials
    • Irreducibility checking
    • Polynomial evaluation by assigning to the invariant (X in this case) a value.
    • All numbers use BigInteger integers, for arbitrarily large numbers.

Polynomial Rings over a Finite Field

  • Polynomial.Field supports all of the above arithmetic operations, but on a polynomial ring over a finite field!

    • What this effectively means in less-technical terms is that the polynomial arithmetic is performed in the usual way, but the result is then taken modulus two things: A BigInteger integer and another polynomial:
      • Modulus an integer: All the polynomial coefficients are reduced modulus this integer.
      • Modulus a polynomial: The whole polynomial is reduced modulus another, smaller, polynomial. This notion works much the same as regular modulus; The modulus polynomial, lets call it g, is declared to be zero, and so every multiple of g is reduced to zero. You can think of it this way (although this is not how its actually carried out): From a large polynomial, g is repeatedly subtracted from that polynomial until it cant subtract g anymore without going past zero. The result is a polynomial that lies between 0 and g. Just like regular modulus, the result is always less than your modulus, or zero if the first polynomial was an exact multiple of the modulus.
      • Effectively forms a quotient ring
  • You can instantiate a polynomial in various ways:

    • From a string
      • This is the most massively-useful way and is the quickest way to start working with a particular polynomial you had in mind.
    • From its roots
      • Build a polynomial that has as its roots, all of the numbers in the supplied array. If you want multiplicity of roots, include that number in the array multiple times.
    • From the base-m expansion of a number
      • Given a large number and a radix (base), call it m, a polynomial will be generated that is that number represented in the number base m.
  • Other methods of interest that are related to, but not necessarily performed on a polynomial:

    • Eulers Criterion
    • Legendre Symbol and Legendre Symbol Search
    • Tonelli-Shanks
    • Chinese Remainder Theorem
Product Compatible and additional computed target framework versions.
.NET net5.0 is compatible.  net5.0-windows was computed.  net6.0 was computed.  net6.0-android was computed.  net6.0-ios was computed.  net6.0-maccatalyst was computed.  net6.0-macos was computed.  net6.0-tvos was computed.  net6.0-windows was computed.  net7.0 was computed.  net7.0-android was computed.  net7.0-ios was computed.  net7.0-maccatalyst was computed.  net7.0-macos was computed.  net7.0-tvos was computed.  net7.0-windows was computed.  net8.0 was computed.  net8.0-android was computed.  net8.0-browser was computed.  net8.0-ios was computed.  net8.0-maccatalyst was computed.  net8.0-macos was computed.  net8.0-tvos was computed.  net8.0-windows was computed. 
.NET Core netcoreapp3.0 was computed.  netcoreapp3.1 is compatible. 
.NET Standard netstandard2.1 is compatible. 
.NET Framework net45 is compatible.  net451 was computed.  net452 was computed.  net46 is compatible.  net461 was computed.  net462 was computed.  net463 was computed.  net47 was computed.  net471 was computed.  net472 was computed.  net48 is compatible.  net481 was computed. 
MonoAndroid monoandroid was computed. 
MonoMac monomac was computed. 
MonoTouch monotouch was computed. 
Tizen tizen60 was computed. 
Xamarin.iOS xamarinios was computed. 
Xamarin.Mac xamarinmac was computed. 
Xamarin.TVOS xamarintvos was computed. 
Xamarin.WatchOS xamarinwatchos was computed. 
Compatible target framework(s)
Additional computed target framework(s)
Learn more about Target Frameworks and .NET Standard.

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Version Downloads Last updated
2023.122.1339 172 5/2/2023
2022.322.2016 312 11/19/2022
2022.322.1953 277 11/19/2022
2022.321.408 296 11/17/2022
2022.195.1511 430 7/14/2022
2022.187.1018 407 7/6/2022
1.0.0 457 11/30/2020